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  2. Distance - Wikipedia

    en.wikipedia.org/wiki/Distance

    Manhattan distance on a grid. Unusual definitions of distance can be helpful to model certain physical situations, but are also used in theoretical mathematics: In practice, one is often interested in the travel distance between two points along roads, rather than as the crow flies.

  3. Metric space - Wikipedia

    en.wikipedia.org/wiki/Metric_space

    In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. [1] Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry.

  4. Euclidean distance - Wikipedia

    en.wikipedia.org/wiki/Euclidean_distance

    In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance.

  5. Distance geometry - Wikipedia

    en.wikipedia.org/wiki/Distance_geometry

    Distance geometry is the branch of mathematics concerned with characterizing and studying sets of points based only on given values of the distances between pairs of points. [1] [2] [3] More abstractly, it is the study of semimetric spaces and the isometric transformations between them. In this view, it can be considered as a subject within ...

  6. Distance from a point to a line - Wikipedia

    en.wikipedia.org/wiki/Distance_from_a_point_to_a...

    The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.

  7. Taxicab geometry - Wikipedia

    en.wikipedia.org/wiki/Taxicab_geometry

    This different definition of distance also leads to a different definition of the length of a curve, for which a line segment between any two points has the same length as a grid path between those points rather than its Euclidean length. The taxicab distance is also sometimes known as rectilinear distance or L 1 distance (see L p space). [1]

  8. Lp space - Wikipedia

    en.wikipedia.org/wiki/Lp_space

    In mathematics, the L p spaces are ... The Euclidean distance between two points and is the length ... The mathematical definition of the ...

  9. Wasserstein metric - Wikipedia

    en.wikipedia.org/wiki/Wasserstein_metric

    In mathematics, the Wasserstein distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given metric space. It is named after Leonid Vaseršteĭn .